## Description

 Title: Central extensions of divisible groups Author(s): Elliot, Jason W. Director of Research: Robinson, Derek J.S. Doctoral Committee Chair(s): Mineyev, Igor Doctoral Committee Member(s): Robinson, Derek J.S.; Ivanov, Sergei V.; Ullom, Stephen V. Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): divisible groups central extensions nilpotent groups group extensions Abstract: This thesis contributes to the classification of central extensions of divisible groups with finite abelian quotient, so called d-ab extensions.'' We give a matrix classification of equivalence classes of d-ab extensions and explicitly provide a family of group presentations. We provide a criterion for determining when two d-ab extensions are isomorophic in the case when the quotient is homocyclic. When the kernel has rank 1, we parametrize isomorphism classes of d-ab extensions with homocyclic quotient by constructing a family of group presentations. We also give a general reduction of d-ab extensions to the case when the kernel and center of the extensions coincide. For this case we give a classification of isomorphism classes when the kernel has rank 1. We highlight the applications of central extensions of divisible groups to nilpotent groups. Issue Date: 2011-05-25 URI: http://hdl.handle.net/2142/24095 Rights Information: Copyright 2011 Jason Walter Elliot Date Available in IDEALS: 2011-05-25 Date Deposited: 2011-05
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